Affiliation:
1. Department of Electrical and Computer Engineering , Babol Noshirvani University of Technology , Babol, Mazandaran, Iran
Abstract
Abstract
A hotspot is an axis-aligned square of fixed side length s, where the amount of time a moving entity spends within it is maximised. An exact hotspot of a polygonal trajectory with n edges can be found with time complexity O(n
2). We define a c-approximate hotspot as an axis-aligned square of side length cs, in which the presence duration of the entity is no less than that of an exact hotspot. In this paper we present an algorithm to find a (1 + ϵ)-approximate hotspot of a polygonal trajectory with time complexity
O
(
n
ϕ
ϵ
log
n
ϕ
ϵ
)
O\left( {{{n\phi } \over \varepsilon }\log {{n\phi } \over \varepsilon }} \right)
, where ϕ is the ratio of average trajectory edge length to s.
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